Cloth Simulator gives strange shading
Cloth simulation works best with a 'flat' mesh - rather than one extruded to give thickness - otherwise both 'sides' of the cloth have to be simulated separately and they can overlap (which is, I believe, what you are seeing). If you want to give your cloth thickness, you can add a Solidify modifier below the Cloth modifier in the modifier stack. In this way the cloth simulation will simulate a 'flat' cloth while the solidifier modifier will give it 'thickness', without the possibility of opposite sides intersecting.